Prograde and retrograde precession of a fluid-filled cylinder

We numerically study precession driven flows in a cylindrical container whose nutation angle varies between 60 and 90 degrees for prograde and retrograde precession. For prograde precession we observe sharp transitions between a laminar and a turbulent flow state with low and high geostrophic axisymmetric flow components related with a centrifugal instability, while for retrograde precession a rather smooth transition between a low state and a high state occurs. At the same time prograde and perpendicular precession shows an abrupt breakdown of the flow directly excited by the forcing mechanism, which is not the case for retrograde motion. We characterize the corresponding flow states in terms of the directly driven, non-axisymmetric Kelvin mode, the axisymmetric geostrophic mode, and an axisymmetric poloidal flow which is promising for precession-driven dynamo action. The latter issue is discussed with particular view on an optimal parameter choice for the DRESDYN dynamo project.

Possible Role of Non-Stationarity of Magnetohydrodynamic Turbulence in Understanding of Geomagnetic Excursions

The natural simplifying assumptions often put forward in the theoretical investigations of the magnetohydrodynamic turbulence are that the turbulent flow is statistically isotropic, homogeneous and stationary. Of course, the natural turbulence in the planetary interiors, such as the liquid core of the Earth is neither, which has important consequences for the dynamics of the planetary magnetic fields generated via the hydromagnetic dynamo mechanism operating in the interiors of the planets. Here we concentrate on the relaxation of the assumption of statistical stationarity of the turbulent flow and study the effect of turbulent wave fields in the Earth’s core, which induces non-stationarity, on the turbulent resistivity in the non-reflectionally symmetric flow and the geodynamo effect. It is shown that the electromotive force, including the so-called α-effect and the turbulent magnetic diffusivity η¯, induced by non-stationary turbulence, evolves slowly in time. However, the turbulent α¯ coefficient, responsible for the dynamo action and η¯ evolve differently in time, thus creating periods of enhanced and suppressed turbulent diffusion and dynamo action somewhat independently. In particular, periods of enhanced α¯ may coincide with periods of suppressed diffusion, leading to a stable and strong field period. On the other hand, it is shown that when enhanced diffusion occurs simultaneously with suppression of the α-effect, this leads to a sharp drop in the intensity of the large-scale field, corresponding to a geomagnetic excursion.

Direct statistical simulation of low-order dynamosystems

In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third order and has cubic nonlinearities while the second has only quadratic nonlinearities and describes the interaction of convection and an aperiodically reversing magnetic field. We show how DSS can be used to solve for the statistics of these systems of equations both in the presence and the absence of stochastic terms, by truncating the cumulant hierarchy at either second or third order. We compare two different techniques for solving for the statistics: timestepping, which is able to locate only stable solutions of the equations for the statistics, and direct detection of the fixed points. We develop a complete methodology and symbolic package in Python for deriving the statistical equations governing the low-order dynamic systems in cumulant expansions. We demonstrate that although direct detection of the fixed points is efficient and accurate for DSS truncated at second order, the addition of higher order terms leads to the inclusion of many unstable fixed points that may be found by direct detection of the fixed point by iterative methods. In those cases, timestepping is a more robust protocol for finding meaningful solutions to DSS.

Signature of the turbulent component of the solar dynamo on active region scales and its association with flaring activity

ABSTRACT It is a challenging problem to obtain observational evidence of the turbulent component of solar dynamo operating in the convective zone because the dynamo action is hidden below the photosphere. Here we present results of a statistical study of flaring active regions (ARs) that produced strong solar flares of an X-ray class X1.0 and higher during a time period that covered solar cycles 23 and 24. We introduced a magneto-morphological classification of ARs, which allowed us to estimate the possible contribution of the turbulent component of the dynamo into the structure of an AR. We found that in 72 per cent of cases, flaring ARs do not comply with the empirical laws of the global dynamo (frequently they are not bipolar ARs or, if they are, they violate the Hale polarity law, the Joy law, or the leading sunspot prevalence rule). This can be attributed to the influence of the turbulent dynamo action inside the convective zone on spatial scales of typical ARs. Thus, it appears that the flaring is governed by the turbulent component of the solar dynamo. The contribution into the flaring from these AR ‘violators’ (irregular ARs) is enhanced during the second maximum and the descending phase of a solar cycle, when the toroidal field weakens and the influence of the turbulent component becomes more pronounced. These observational findings are in consensus with a concept of the essential role of non-linearities and turbulent intermittence in the magnetic fields generation inside the convective zone, which follows from dynamo simulations.

Properties of Polarized Synchrotron Emission from Fluctuation Dynamo Action—II. Effects of Turbulence Driving in the ICM and Beam Smoothing

Polarized synchrotron emission from the radio halos of diffuse intracluster medium (ICM) in galaxy clusters are yet to be observed. To investigate the expected polarization in the ICM, we use high resolution (1 kpc) magnetohydrodynamic simulations of fluctuation dynamos, which produces intermittent magnetic field structures, for varying scales of turbulent driving (lf) to generate synthetic observations of the polarized emission. We focus on how the inferred diffuse polarized emission for different lf is affected due to smoothing by a finite telescope resolution. The mean fractional polarization ⟨p⟩ vary as ⟨p⟩∝lf1/2 with ⟨p⟩>20% for lf≳60 kpc, at frequencies ν>4GHz. Faraday depolarization at ν<3 GHz leads to deviation from this relation, and in combination with beam depolarization, filamentary polarized structures are completely erased, reducing ⟨p⟩ to below 5% level at ν≲1 GHz. Smoothing on scales up to 30 kpc reduces ⟨p⟩ above 4 GHz by at most a factor of 2 compared to that expected at 1 kpc resolution of the simulations, especially for lf≳100 kpc, while at ν<3 GHz, ⟨p⟩ is reduced by a factor of more than 5 for lf≳100 kpc, and by more than 10 for lf≲100 kpc. Our results suggest that observational estimates of, or constrain on, ⟨p⟩ at ν≳4 GHz could be used as an indicator of the turbulent driving scale in the ICM.

Kinematic dynamos in triaxial ellipsoids

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

Anisotropic diffusivities' effects in rotating magnetoconvection and geodynamo problems

&lt;p&gt;There are many examples which show&amp;#160;how the anisotropic diffusive coefficients&amp;#160;crucially influence&amp;#160;geophysical and astrophysical flows and in particular&amp;#160;flows in the Earth&amp;#8217;s outer core. Thus, many&amp;#160;models concerning rotating magnetoconvection with anisotropy in the viscosity, thermal and magnetic diffusivities have been developed. &amp;#160;&lt;/p&gt;&lt;p&gt;Different models correspond to different cases of anisotropic diffusivities. For example, we consider several anisotropic models: one with anisotropy in all diffusivities and other models with various combinations of anisotropic and isotropic diffusivities. &amp;#160;&lt;/p&gt;&lt;p&gt;Firstly, all kind of anisotropies are reminded and described. Then, a thorough comparison of these anisotropies, especially of the physical differences among them is&amp;#160;done. All physical systems with the above mentioned anisotropies are prone to the occurrence of convection and&amp;#160;other instabilities. We show how different types of anisotropy cause a different convection and a different balance among the main forces in the Earth&amp;#8217;s Outer Core (Magnetic, Archimedean, Coriolis). &amp;#160;&lt;/p&gt;&lt;p&gt;As usually, to study instabilities in such systems, we use analysis in term of normal modes and search for preferred modes. In all our models, only marginal modes with zero growth rate have so far been studied. Now, we present the bravest modes, i.e. the ones with maximum growth rate. The comparison of the modes dependent on basic input parameters - Prandtl numbers, anisotropic parameter, Ekman and Elsasser numbers - is made mainly for values corresponding to the Earth&amp;#8217;s outer core.&amp;#160;In all our&amp;#160;models the anisotropic diffusive coefficients are represented as diagonal tensors with two equal components different from the third one&amp;#160;giving the chance to define simply the anisotropic parameter. &amp;#160;&lt;/p&gt;&lt;p&gt;We stress how magnetoconvection problems&amp;#160;with&amp;#160;the anisotropy&amp;#160;included, became more and more important among the geodynamo problems in the last years; indeed, the origin of flows necessary for dynamo action, as studied in magnetoconvection with resulting instabilities, is important, as well as the problem of the origin of magnetic fields. &amp;#160;&lt;/p&gt;